posted by Elisa .
An airplane flies 200 km due west from city A to city B and then 280 km in the direction of 30.5° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?
how many° north of west
(1) Add the vector going from A to B and the vector going from B to C. The length of the resultant vector will tell you the distance from A to C.
(2) The direction of the resultant vector of step 1 is what you are looking for. The angle (measured north from west) is arctan (Change in y)/(-Change in x)
= arctan (280 sin 30.5)/(200 + 280 cos 30.5) = arctan [142.1/(200 +241.2)]